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The disciminat of the quadratic formula must = 0 for this to be true

b^2 - 4ac = 0   

b^2 - 4(1)16) = 0

b^2 = 64

b = +- 8

We  have  a triangle  that  makes up the  bottom of the figure  with   a  base of 13  and an altitude of 11.3

Its  area is    (1/2)(13)(11.3)   =   73.45 cm^2

Then we  have  three congruent triangles making up  the  sides  with bases of 13 and  heights  of 9

Their combined area   is   3 (1/2) ( 13) (9) =175.5 cm^2

So....the total surface area =  73.45  + 175.5    = 248.95 cm^2

ANSWER IS 15,600

Here's my solution from a while  back  :

For simplicity, let's suppose that there are 100 kids at the school

If 8% bring both, then 8 bring both

Let the number who bring raincoats = x

Let the number who bring umbrellas =  2x

So....the ones that bring only raincoats = x - 8

And the ones that bring only umbrellas = 2x - 8

So......we have this equation

Kids who bring only umbrellas + kids who bring both + kids who only bring raincoats = 100

(2x -8)  +  8  + (x - 8)  =  100      simplify

3x - 8   = 100      add 8 to both sides

3x = 108      divide both sides by 3

x = 36

So....the ones who bring only a rain coat =  36 - 8  =  28

And the ones who bring only an umbrella  = 2(36) - 8  =  72 - 8  = 64 = 64%

Check

Only umbrellas +  Both + Only Raincoats = 100  ???

64  +  8  +  28   =  100   (Check)

log₁₆ 49  = a          log ₇  2.5    = b 

Using  the  change  of  base theorem

ab +  1  =

log 49           log 2.5

_____  *    ________    +   1

log 16           log 7

log 49           log 2.5          

_____  *     _______   +     1

log 7             log 16

log 7^2           log 2.5        

______  *     ________ +    1

log 7               log 4^2

2log 7          log 2.5

_____ *      _______   +    1

log 7            2log 4

2  *             log  (10/4)

             __________    +     1

                    2log 4

log 10  -  log 4

___________      +     1  

     log 4

log 10        log 4

_____   -  ______    +   1

log 4         log 4

1 / log 4  -  1  +   1

1/log 4

So.....    using a  log property that  a^ (1/log a)   = 10.....then

4^(ab + 1)  = 4^ (1/log 4)  =    10

By similar triangles, [PAB]/[QAB] = 3/7.

A/B = 8/7.

Thank you!!!

reflect the graph over the x-axis

translate the graph down

stretch the graph away from the x-axis

We have  that 

 AD  / AC =   DE  / BC

8 /12 =  DE  /   15

2/ 3 =  DE  / 15  multiply both sides by 15

15 * 2  / 3  =  DE

30  / 3  =  DE

10  = DE  =  x

Tell me if it's correct

2*(1+2+3+4+5+6+7+8+9)=90, 9

Something else I thought of:

For the white balls, you just need to get 2 wrong to not get the super prize.  To get 1 wrong is 9/10.  To get 2 wrong is 81/100.  Is there a 9/10*81/100 chance of not getting a super prize or did I make a mistake somewhere?

Amt left  after buying a notebook=   19  - 7.25  = 11.75

If  he  needs  to  save 2.75, then he has    11.75 - 2.75  = $9  left to spend

So...let  P  bet  the number of packages he could buy

.50P  ≤  9     ⇒  the    inequality     ....divide both  sides by .50

P ≤   18    .......he  can  buy up to 18 packages

Let the cost of one hat =  H

Let the cost of  one  T-Shirt   = T

So  we have this system

4T  +  2H  =  10              divide  through by  2 ⇒       2T  + H   = 5   ⇒   H =  5  - 2T     (1)

3 T +  3 H =  11.25             (2)

Sub (1)  into  (2)  for H

3T  +  3( 5 -2T)=   11.25

3T  + 15  - 6T  =11.25

-3T + 15   =11.25

-3T  =  11.25   -  15

-3T  =  -3.75               divide  both  sides by  -3

1.25  =  cost  of a T-Shirt

H  = 5 - 2(1.25)  =    5  - 2.50   = 2.50    = cost  of a  hat

Bag A contains 3 white and 2 red balls. Bag B contains 6 white and 3 red balls. One of the two bags will be chosen at random, and then two balls will be drawn from that bag at random without replacement. What is the probability that the two balls drawn will be the same color? Express your answer as a common fraction.

Question said to round to the nearest whole number, Silly !

Thank you.

How many of each red and white balls are in the bags??

To be sure, 15,267.35 ...  what is .35 of a person? ... maybe there's an expectant mother about 3 months along ....

The three angles labelled at the bottom of the diagram add up to a straight line ====> 180 ⁰

4x-8        +    34       +    76-x       = 180

3x = 78

x = 26

Final mixture is 120 gm

x = 10%      then   (120-x) = 25%

.25(120-x)    + .1 (x)    =  .15 (120)       solve for x= 10% amount

                                                                  then  25% amount = 120-x

ingredients in = ingredients out

.4 (80)   +  x (60) =  .55 (80+60)

x= .75     or 75%

Use cos rule

93^2 = 82^2 +86^2 - 2 (82)(86) cos J      solve for J

(93^2 - 82^2 -86^2)/ ((-2)(86)(82)] = Cos J    

J =~ 67^o

I don't have time to write a full solution, but the expression simplified to 3.